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At what temperature will He atoms have t...

At what temperature will He atoms have the same r.m.s. speed as `H_(2)` molecules have at `27^(@)C`?

Text Solution

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`U_(RMS) = sqrt((3RT)/(M))`
`U_((H_(2))) = sqrt((3RT)/(2.0)) = sqrt((3R xx 300)/(2.0))` [Gram molecular mass of `H_(2) = 2.0 g mol^(-1)`]
`U_((He)) = sqrt((3RT)/(4.0))` [Gram atomic mass of `He = 4.0 g "atom"^(-1)`]
According to the available data :
`U_((H_(2))) = U_((He)) :. sqrt((3R xx 300)/(2.0)) = sqrt((3RT)/(4.0))`
Square both sides, `(3R xx 300)/(2.0) = (3RT)/(4.0)` or `T = 600 K` or `t = 600 - 273 = 327^(@)C`
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